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Let’s check out your problem:

(a) Write as a single fraction: (2x+3)/(3)+(x-4)/(4)

(a) Write as a single fraction:\newline2x+33+x−44\frac{2x+3}{3}+\frac{x-4}{4}

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Full solution

Q. (a) Write as a single fraction:\newline2x+33+x−44\frac{2x+3}{3}+\frac{x-4}{4}
  1. Find LCD: To combine the two fractions, we need to find a common denominator. The denominators here are 33 and 44, so the least common denominator (LCD) is 1212.
  2. Adjust fractions: Now we need to adjust each fraction so that they both have the denominator of 1212. To do this, we multiply the numerator and denominator of the first fraction by 44 and the numerator and denominator of the second fraction by 33.
  3. Simplify fractions: After adjusting the fractions, we have:\newline(2x+3)/3×4/4+(x−4)/4×3/3(2x+3)/3 \times 4/4 + (x-4)/4 \times 3/3\newlineThis simplifies to:\newline(8x+12)/12+(3x−12)/12(8x+12)/12 + (3x-12)/12
  4. Add numerators: Now that both fractions have the same denominator, we can add the numerators together:\newline(8x+12)+(3x−12)=8x+12+3x−12(8x+12) + (3x-12) = 8x + 12 + 3x - 12
  5. Combine like terms: Combine like terms in the numerator: 8x+3x+12−12=11x8x + 3x + 12 - 12 = 11x
  6. Final fraction: The final single fraction is: 11x12\frac{11x}{12}

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